Kontsevich's conjecture. Category theoretic mirror symmetry conjecture. Revised

Kontsevich's conjecture. Category theoretic mirror symmetry conjecture. Revised

TANAKA Akio

When there exists mirror relation between X1 and X2, derived category of X1's  coherent sheaf  and derived Fukaya category defined from X2's symplectic structure become equivalence.

M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.

-----------------------------------------------------------------------------------------------------------------------

[Note by TANAKA Akio]

In the near future, symplectic geometry may be written by derived category. If so, complex image of symplectic geometry's some theorems may be become more simple and clear than now. 

References

Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory / 27 February 2009
Homological Mirror Symmetry Conjecture by KONTSEVICH
    / Symplectic Language Theory / 26 April 2009​
Quantization of Language / Floer Homology Language / 24 June 2009

Tokyo

10 May 2016
SRFL Theory

Also refer to the next..
Derived Category Language, 23 July 2016 Edition

Tokyo
26 July 2016
Sekinan Library